None of the videos I watched mentioned multiple bikes, but if you wanted to use the Mini, on more than one bike, you would have to move the sensors from bike to bike, unless the phone app allows you to turn off each speed and cadence sensor with toggle. I have a BlueSC sensor on my bike and have two RPM sensors pared to my phone for when I ride my wife's trike. I have to turn off my BlueSC before turning on the RPM sensors or the phone app gets confused as to which sensor to use and ends up using none of them. Both the RPM sensors are easy to move from bike to bike since they don't need tie wraps to hold them in place. You should be able to change wheel size in the app, but I would verify that first.
The Mini does not have GPS, period. It connects to the sensors by Ant+, which is why you need the dual band sensors. It is basically a stand alone Ant+ computer. You do not need a phone connected to the Mini in order to use it. If it's connected to the phone, the phone app tracks the route using the phone's GPS and stores all the ride data. The phone app will also connect to the sensors via BTLE and use the data from the sensors to make the GPX file. When you send your ride to Strava or other site, via the phone, the complete GPX file is send, including the map and route. If you aren't going to use the phone to track your ride, the only reason to connect it is to change fields, add new pages and change parameters on the Mini.
As for the battery, if you don't keep the screen turned on, the battery should hold for up to 8 hours, depending on your phone. I can do a century without having to charge my iPhone SE that's connected to a speed cadence, heart rate and RFLKT sensor.